Calculating a PCA and a MDS on a fingerprint data set

Transcription

1 BioNumerics Tutorial: Calculating a PCA and a MDS on a fingerprint data set 1 Aim Principal Components Analysis (PCA) and Multi Dimensional Scaling (MDS) are two alternative grouping techniques that can both be classified as dimensioning techniques. In contrast to dendrogram inferring methods, they do not produce hierarchical structures like dendrograms. Instead, these techniques produce two dimensional or three dimensional plots in which the entries are spread according to their relatedness. Unlike a dendrogram, a PCA or MDS plot does not provide clusters. The interpretation of the obtained comparison is, more than in cluster analysis, left to the user. In this tutorial you will learn how to create a PCA and MDS and how to change the layout of the obtained plots. Multi Dimensional Scaling (MDS) is sometimes also called Principal Coordinates Analysis (PCoA). 2 Preparing the database The DemoBase Connected will be used in this tutorial and can be downloaded directly from the BioNumerics Startup window or restored from the back-up file available on our website: 1. To download the database directly from the BioNumerics Startup window, click the Download example databases link, located in the lower right corner of the BioNumerics Startup window. Select DemoBase Connected from the list and select Database > Download. Confirm the download action. 2. To restore the database from the back-up file, first download the file DemoBase Connected.bnbk from under DemoBase Connected. In the BioNumerics Startup window, press the button, select Restore database, browse for the downloaded file and select Create copy. Specify a name and click <OK>. In contrast to other browsers, some versions of Internet Explorer rename the DemoBase Connected.bnbk database backup file into DemoBase Connected.zip. If this happens, you should manually remove the.zip file extension and replace with.bnbk. A warning will appear ( If you change a file name extension, the file might become unusable. ), but you can safely confirm this action. Keep in mind that Windows might not display the.zip file extension if the option Hide extensions for known file types is checked in your Windows folder options. 3 Principal components analysis (PCA) Principal components analysis (PCA) is another way to visualize relationships among entries. Unlike a Multi Dimensional scaling (MDS), PCA uses the data set itself instead of the similarity matrix to measure

2 2 relatedness. PCA maximizes the variation among entries along the first two or three dimensions, which can then be displayed. These are the principal components. 1. Open the DemoBase Connected by double-clicking on this database in the BioNumerics Startup window. 2. In the Database entries panel of the Main window, select all entries using the Ctrl+A keyboard shortcut. Unselect the three entries defined as STANDARD by unchecking the check boxes next to the entries. Alternatively use the space bar or use the Ctrl-key. 3. Highlight the Comparisons panel in the Main window and select Edit > Create new object... ( ) to create a new comparison for the selected entries. 4. Click on the next to the experiment name AFLP in the Experiments panel to display the data in the Experiment data panel. Since fingerprints can only be analyzed by PCA after a band matching table is generated, we will first perform a band matching: 5. Select Fingerprints > Perform band matching... ( ). 6. Select Find classes on all entries and press <OK>. Next, we will create groups based on the content of the Genus database field. 7. Click on the database field Genus in the Information fields panel. 8. Select Groups > Create groups from database field and press <OK>. Group colors are now assigned to the different Genus groups. 9. Make sure AFLP is selected in the Experiments panel and select Statistics > Principal Components Analysis... ( ). 10. Press <OK> to start the calculation of the PCA. The Principal Components Analysis window is divided in different panels (see Figure 1): The Entry coordinates panel shows the entries plotted in an X-Y diagram corresponding to the first two components. In the Components panel, the first 20 components are shown, with their relative contribution and the cumulative contribution displayed. Also, the components used as X, Y and Z axes are indicated. The Character coordinates panel shows the characters plotted in the same X-Y diagram showing the contribution that each character has to the two displayed components, and hence, what contribution it has to the separation of the groups along the same components. The Components panel lists the principal components in the order of their contribution to overall variance. The components used as X, Y and Z axes are also indicated. A band class that appears near the edge of the plot is a strong discriminator, while a band class near the center is a weak discriminator. Furthermore, a band class that appears near the position of an entry is an indicator for that entry. 11. Switch from color indication for the groups to symbol indication with Layout > Show color coding ( ). 12. Show the keys or a unique label based upon the groups for the entries with Layout > Show keys ( ). 13. With Layout > Zoom in / zoom out ( ), you can zoom in on any part of the entries or characters panel of the PCA plot: drag the mouse pointer to create a rectangle; the area within the rectangle will be zoomed to cover the whole panel.

3 4. Multi Dimensional scaling (MDS) 3 Figure 1: The Principal Components Analysis window. 14. In order to restore the original size of the image, simply left-click within the panel. Disable the zoom mode afterwards. 15. Entries can be selected in an Entry coordinates panel by holding the Shift-key down and selecting the entries in a rectangle using the left mouse button. Selected entries are encircled in blue. 16. Press F4 to unselect all entries. 17. If you move the mouse pointer over the characters in the Characters coordinates panel, the name of the pointed character is shown. 18. The entry plot can be printed with File > Print image (entries)... ( ) and the character plot can be printed with File > Print image (characters) Alternatively, the entry plot can be copied to the clipboard with File > Copy image to clipboard (entries)... ( ) and the character plot can be copied to the clipboard with File > Copy image to clipboard (characters). 20. To create a three-dimensional plot from the PCA, select Layout > Show 3D plot ( ). See 5 for more information about this 3-D representation. 21. Close the windows with File > Exit. 4 Multi Dimensional scaling (MDS) Multi Dimensional scaling (MDS) is an optimized three-dimensional representation of the similarity matrix. The Euclidean distance between two points (entries) reflects the similarity between them as well as possible, while providing a convenient visual interpretation. A similarity matrix must be present before an MDS can

4 4 be calculated. 1. Select AFLP in the Experiments panel of the Comparison window and calculate a dendrogram based on the Pearson correlation with Clustering > Calculate > Cluster analysis (similarity matrix) If group colors are no longer available, proceed as described in 3 to create groups based on the Genus field. 3. Select Statistics > Multi-dimensional scaling... ( ). 4. Check Optimize positions and press <OK> to start the calculations. The MDS is calculated and the Coordinate space window is shown (see Figure 2). The Coordinate space window shows the entries as dots in a cubic coordinate system. Figure 2: The Coordinate space window. 5 Changing the coordinate space layout 1. To zoom in or zoom out on the image, use Layout > Zoom in (Pge Down) or Layout > Zoom out (Pge Up), respectively. 2. The image can be rotated in real time by dragging the mouse pointer in any direction. The entries are represented as small dots, in the colors as defined in the Comparison window. 3. With Layout > Show keys ( ), you can display the database keys of the entries instead of the dots. Entry keys may be long and uninformative for the user. The entry keys can be replaced by a group code: an alphabetical numbering of groups with an index per entry in a group. The group codes are shown as follows: 4. In the Comparison window, select Layout > Use group numbers as key. 5. A list of entry indices as used in the PCA and the corresponding entry names can be obtained by selecting File > Export > Export database fields... in the Comparison window. 6. Alternatively, you can select a field in the Comparison window, for example the Strain number field, and select Layout > Use field as key.

5 5. Changing the coordinate space layout 5 7. With Layout > Show group colors ( ), you can toggle between the color representation and the noncolor representation. 8. With Layout > Show construction lines ( ), the entries are displayed on vertical lines starting from the bottom of the cube. 9. Layout > Show rendered image ( ) displays the coordinate system in realistic three-dimensional perspective. 10. Another very interesting option is Layout > Show dendrogram ( ). The entries in the coordinate system are connected by the branches of the dendrogram that was calculated in the Comparison window (see Figure 3). This is an ideal combinatation to co-evaluate a dendrogram and a coordinate system. Figure 3: Co-evaluation of a dendrogram and a coordinate system. 11. The image can be printed with File > Print image... ( ). The image will print in color if the colors are shown on the screen.